Responses of Halo Occupation Distributions: a new ingredient in the halo model & the impact on galaxy bias

Abstract

Halo occupation distribution (HOD) models describe the number of galaxies that reside in different haloes, and are widely used in galaxy-halo connection studies using the halo model (HM). Here, we introduce and study HOD response functions $R_{\mathcal{O}}^g$ that describe the response of the HODs to long-wavelength perturbations $\mathcal{O}$. The linear galaxy bias parameters $b_{\mathcal{O}}^g$ are a weighted version of $b_{\mathcal{O}}^h+R_{\mathcal{O}}^g$, where $b_{\mathcal{O}}^h$ is the halo bias, but the contribution from $R_{\mathcal{O}}^g$ is routinely ignored in the literature. We investigate the impact of this by measuring the $R_{\mathcal{O}}^g$ in separate universe simulations of the IllustrisTNG model for three types of perturbations: total matter perturbations, $\mathcal{O}={\delta }_m$; baryon-CDM compensated isocurvature perturbations, $\mathcal{O}=\sigma$; and potential perturbations with local primordial non-Gaussianity, $\mathcal{O}\propto f_{\mathrm{NL}}\varphi$. Our main takeaway message is that the $R_{\mathcal{O}}^g$ are not negligible in general and their size should be estimated on a case-by-case basis. For stellar-mass selected galaxies, the responses $R_{\varphi }^g$ and $R_{\sigma }^g$ are sizeable and cannot be neglected in HM calculations of the bias parameters $b_{\varphi }^g$ and $b_{\sigma }^g$; this is relevant to constrain inflation using galaxies. On the other hand, we do not detect a strong impact of the HOD response $R_1^g$ on the linear galaxy bias $b_1^g$. These results can be explained by the impact that the perturbations have on stellar-to-total-mass relations. We also look into the impact on the bias of the gas distribution and find similar conclusions. We show that a single extra parameter describing the overall amplitude of $R_{\mathcal{O}}^g$ recovers the measured $b_{\mathcal{O}}^g$ well, which indicates that $R_{\mathcal{O}}^g$ can be easily added to HM/HOD studies as a new ingredient.

22 pages, 12 figures, 1 table. Comments are welcome! Accepted by JCAP

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